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# Carbon Fiber prosthetic foot - STIFFNESS

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## Carbon Fiber prosthetic foot - STIFFNESS

(OP)
I have made a FEM model of a prosthetic foot. And i want to obtain the stiffness of the model.
I´m thinking of doing a Force vs Displacement graph, but i´m still not sure how to accomplish my purpose.
I need some help.

### RE: Carbon Fiber prosthetic foot - STIFFNESS

i think u can apply a load of 1 newton and read the displacement thus get the stiffness :1/displacement.

### RE: Carbon Fiber prosthetic foot - STIFFNESS

What do you need the stiffness for?

You will probably need to estimate the center of area of the load on the base of the foot. In an extreme case that can need a contact analysis. However, an initial estimate can be made based on common sense and observations of how the ground exerts load on the soles of feet. Once you've got the C of A you can do simple calculations for a unit load on that C of A and whatever constraints you decide on for how the foot is connected to the ankle and leg. However, depending on what you need the deflection for it may be necessary to apply a distributed load to capture the details of the deformation of the foot structure. This probably depends on what the foot's structure looks like. It is common for feet to be designed as blades. Is your foot this simple or is it more complicated?

### RE: Carbon Fiber prosthetic foot - STIFFNESS

(OP)
Hi,
RPstress
http://www.medicalexpo.com/prod/ossur/product-7494... (the design is very similar)
My foot is still very simple, because i´m in the earliest part of the design. I am not only designing the blade, but also the socket of the prosthesis (bone, soft tissue, liner made of silicone rubber and a carbon fiber socket), and the union.
Now i´m running static analysis of the carbon fiber blade. (i have chosen a laminate of [0,45,0,-45,0] 0(tape), 45,-45 (fabric). It´s an aeronautic material (less than 0,2mm each layer).
I have constrained a contact surface, and i have applied a load in a point in which the socket is placed, and i have transmited the load with a distributing coupling to 4 bolts.
The aim of my university research project is to improve the way the prosthetic foot returns the energy stored. I want to know the stiffness of the blade to compare it with others i have collected from some thesis. Today i have achieved to get the global stiffness matrix from abaqus, and for tomorrow i want to get the reduced or condensed matrix (i don´t know how to do it yet, but i´m trying to make a substructure).
Then i will try to obtain the energy graphics (with a dynamic analysis i suppose).

Hi Jason8zhu,

I will follow your advice, but the problem is that the material is non linear. you gave me an idea, i will make it piecewise.

Sorry if i don´t explain myself correctly, i´m trying to improve my english skills, if you don´t understood something, tell me and i will exert myself more.

Than you very much indeed, Jason8zhu and RPstress, all your advices are very valuable for me.

### RE: Carbon Fiber prosthetic foot - STIFFNESS

So you're working on designing a prosthesis and want it optimized to some degree for the highly dynamic case of running. I would expect there to have been a lot of advanced explicit FE work on this. If you are not able to access this it will be a very difficult process to 'reinvent the foot'.

Thanks for that video; it has enough info to do some very rough static analysis.

A quick search on FE ANALYSIS OF PROSTHETIC FOOT gave a lot of fairly advanced-looking hits for places like http://www.ncbi.nlm.nih.gov/pubmed/12623440. There is indeed a lot of advanced analysis out there.

You're suggesting a layup of 8 plies of material (maybe 1.7 mm thick if the cloth is a bit thicker than the 0.2 mm suggested); it looks a bit mean to me (probably not adequate statically). If there is 450 N in one leg with a dynamic factor of 2 (it'll probably be more) then 450 * 2g * 150 mm lever arm = 135 kN.mm...with a 70 mm wide sole that'll give a stress of 4000 MPa (135000*1.7/2/1.7^3/70*12)... For material subject to severe impacts we use about 275 MPa (on a good day) in aerospace... + there's very excessive static deflection predicted for that sole. Very roughly thickness might need to go up maybe 2.5 times...? I don't know what allowables you can work to. Maybe a fatigue allowable of 1000 MPa in tension and 800 MPa in compression... that should give a life of about 5,000,000 cycles with no initial damage. Well, maybe doubling that thickness might do? Your call (and you'll have control of the analysis which shows it good).

Good luck.

### RE: Carbon Fiber prosthetic foot - STIFFNESS

(OP)
Hey RPstress,
All your suppositions in the matter of loads are correct. Just a correction.. My prosthetic foot is designed for running, and if you examine the gait analysis you will see the phases of running. When we run there is a moment that both feet are in the air, so, the load that we have to consider is not half the weight, but the weight entirely. Then, i´ve divided the cicle of running into 3 phases. Heel strike, mid-stance and toe-off. Each one has different boundary conditions.

You are correct when you suggest that only with 2 layers the foot won´t resist statically.
To run the easy design for a fast running of the calculations, i´ve splitted the prosthesis into 3 parts.
The base of the foot with 25mm, the curvature with 40mm and the upper part with 55mm. if you multiply the thickness by 5, as you have said, we obtain the number of layer.
Do you think that i should do a fatigue analysis?
I think that the dynamic analysis would be interesting in the case of a free fall. I´m still not able to run the entire stride with my knowledge. Inertia effects should be considered and i have still difficulties to put velocities. I
If i wanted to obtain graphs of energies, to see how the prothesis stores and returns energy, which type of analysis should i run? With a static analysis would be enough?

Thank you!!

### RE: Carbon Fiber prosthetic foot - STIFFNESS

You analysis strategy seems sensible. I've never analysed a human limb and I don't know what the people who do so actually do. It would pay to do a bit of research and maybe talk to some of those who do the analysis.

450 N was my guess for an example (100 lb) at a thin athlete's weight (maybe the woman shown in the video). I would expect an actual athlete (even a smallish woman) to weigh quite a bit more. I assume you have all this sorted out for your basic requirements. (If you want to cater for a fat unfit stress engineer (like me) you should be using at least 100 kg as the basic mass, and I suspect that a lot of large fit athletes weight about that—they've probably got as much muscle as I have fat. One of those rail-thin distance runners (who have to put on a pullover if the temperature gets less than 78°F) might weigh a bit less.)

The dynamic factor when running should be more than 2—the dynamic factor for a walk might be as low as 2 (just a guess). If you're doing a dynamic analysis with the right inertia (and a little bit of damping in there somewhere—not at all sure about damping for human bodies) this should be in the mix and the load should be derived from the analysis with appropriate accelerations. The only reason I used a factor was for a rough (quick) static analysis check on suggested thickness before anything more complicated had been done. It always pays to have some simple numbers to bound the problem and act as a sanity check on more black-box FE analysis. A dynamicist might have some rough dynamic analysis to hand. I would expect an implicit dynamic analysis to be adequate, but I also suspect that people are doing explicit analysis with the like of Abaqus Explicit and Dyna. You could use some simple hand analysis for an initial guess at what to analyse first, then mod it based on the early results with a bit of tweaking as the analysis standard improves.

Usually the static allowables for carbon allow for some damage which gives some protection from fatigue, partly because carbon is pretty fatigue resistant even with a bit of damage. My fatigue allowables came from a spreadsheet called "SNL/MSU/DOE COMPOSITE MATERIAL FATIGUE DATABASE" which references http://www.coe.montana.edu/composites and http://windpower.sandia.gov/ . That's where I probably got it (I was probably Googling for fatigue carbon composite or something but that was a year or so ago). Running is unquestionably a fatigue load. 1000 hours of running will give several million cycles. Many runners will do at that in a year. I would guess that most strides will be very similar so there's no issue with a few very high loading cycles and a lot of less significant ones. You probably need a worst case analysis of a typical stride. I'm not sure how to do a static analysis for a nonrecurring bad stride such as coming down on a bad piece of ground like a kerb edge or a rock on one side of the foot. Probably take the load you come up with and bias it well to the edge of the beam, but there may also be significant sideways loading (judging by that video you need a bit of side load in the typical stride). Up to you to determine such a worst case footfall to check statically.

### RE: Carbon Fiber prosthetic foot - STIFFNESS

(OP)
Thanks!!!!

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